Don Page

Lightman:

I'd like to start by asking you to tell me a little bit about your parents.

Page:

My parents were elementary school teachers. After they got married and after my father worked a year in Kansas City, he got tired of commuting and they both wanted to go off somewhere. So they applied to the Bureau of Indian Affairs to go teach in some remote place. They got a position up in Alaska. In 1941, they went to Alaska with the goal of staying a year. But then the US got into World War II, and they were frozen to their jobs. Then I came along at the end of 1948. So, in a sense, I think when they went up there, they were, well, almost pioneers. They had gone out to villages where there weren't any roads and weren't any telephones.

Lightman:

What kind of work did they do in Alaska?

Page:

They taught elementary school. The Bureau of Indian Affairs had schools out in these small villages, varying from 100 to 300 people. In the early stages, my parents had to do a lot of other things, too. In some villages, they were the postmaster or would do [things] if some medical services were needed in the village, minor things at least. They might give shots and various small things, because we would be away from where doctors were. So they were quite independent. They were out there from 1941, and [it was] several years before they even left Alaska, just to see anything. They had fallen in love with it by the time the war was over, so they just stayed.

Lightman:

So you grew up there?

Page:

Right. I grew up there. I was in Alaska all my life until I went to college. Then my parents retired in 1972, after I'd been at Caltech one year.

Lightman:

Can you tell me a little bit about your childhood — what kinds of things you liked to do.

Page:

Of course, Alaska was good for various outdoor things. In the summertime, we would go boating. In most villages, my father would build a boat and we'd go with a motor boat. In wintertime, we'd go skiing. Occasionally — my brother and I had a couple of dogs which we didn't train too well — we'd go dog-sledding or have the dogs pull us on skis. In the summertime, we might go fishing or hiking up mountains and such things. Winter times tended to have fairly long nights. I did some photographic work and developed and enlarged photographs, and that took a lot of evenings in winter. I remember in the earliest days, my mother was fairly mathematical. Both my parents had a college education and a little bit of graduate work beyond, but not enough for another degree. They taught me a lot when I was a child. I can still remember a big board, maybe about two feet by three feet, [on which] my father had written all the numbers out from one up to 100. I don't remember exactly when this was, but it was somewhere between the ages of three and six. It's rather amusing. I still sort of visualize the numbers from one to 100 more or less how they're arranged on this chart. I sort of have a visualization — more, I suppose in dates. I can see the numbers going down, and I think of 1988 very near the bottom of the next to the last column of the chart [for the 20th century]. So [my parents] did a lot of work with me when I was a preschooler.

Lightman:

In mathematics?

Page:

Math was one of the things that I had an early aptitude for, and so I think they helped me some. Neither of them knew advanced math. Algebra, I think, was about as far as they'd gone. So, maybe, I got off on my own. I remember the fifth grade had a solid geometry book that I quite enjoyed playing around with and just reading. It was having fun.

Lightman:

That certainly was not your fifth grade textbook.

Page:

No, this wasn't. [Laughter]

Lightman:

That sounds a little advanced.

Page:

Yes, I think I read it. I don't think I did any of the problems or did the proofs or anything.

Lightman:

Did geometry appeal to you particularly? That kind of structure, that style of doing mathematics, the lemma-proof approach?

Page:

The kind of geometry that I got in high school — proving things by angles and stuff - didn't appeal to me too much. When I got to analytic geometry, Cartesian geometry, which was much more appealing. I never really thought about it, but the analytic kind [of geometry] was [more appealing]. I think in the eighth grade I knew the definition of an ellipse as points [for which] the sum of the distances from the two foci was a constant. I was trying to prove that that was an elongated circle, and I never succeeded, but this was before I knew anything about analytic geometry. So I didn't have any real hopes of writing down equations, but I tried drawing lines and stuff and I never succeeded in proving that. So it fascinated [me]. In those days, they had these big paperback books called Everything Made Simple. I know when I was about ten, I was enthralled with chess, and it was Chess Made Simple. Then, in about the beginning of high school, I got some of the Advanced Mathematics Made Simple [books]. There was one about analytic geometry, I think, and then some other one about linear equations and using determinants to solve linear equations, and a few others of that sort. Most of those things in math I probably learned from books [on the side], before they were really covered in school.

Lightman:

Do you remember any reading in science that you did at this time?

Page:

I do remember reading a certain amount, perhaps in chemistry — although that's a bit paradoxical because I never had a chemistry course in my life. One of my aunts gave me a chemistry set that I played around with a little bit when I was maybe ten. I do remember reading some books early on. I think [when] I was about nine, I'd been reading some things for a while and I suddenly discovered that photons were not the same as protons. I had looked at the word and got them confused. At the early stages, I was probably more interested in math than science per se, although I did have a little bit of interest [in science]. Some of the things in nuclear physics sounded sort of fascinating, although I was a little disturbed that the only application I knew was to make bombs.

Lightman:

Where would you have heard about nucler physics at this age?

Page:

Probably from books, or maybe some encyclopedias. Oh, I do remember one article that was rather seminal in generating interest. The Saturday Evening P08t had a series about the great ideas or something like that. I never really went back to [find out] exactly when that was, but I think it was around when I was ten. It's a little hard for me to remember which one, but one of the [articles] I do remember was on the origin of the elements, [written by] Willy Fowler.^[1] I remember that [article] had a deep impression on me — particularly [the notion of] hydrogen turning to helium in the sun and so on. When I was taking Fowler's course at Caltech, I remembered that article. So I guess there was a certain amount of science besides mathematics in the early stages, but I probably didn't actually decide to go into physics rather than mathematics until I went to college.

Lightman:

I'd like to ask you about that in a minute. Just before we leave this period of time, do you remember at this age having any cosmological thoughts?

Page:

It's a little hard for me to remember whether I had any cosmological [ideas]. I think I had my own theory of elementary particle physics. I thought everything was made of little tiny things. I called them "nuttons," and they were supposed to be little things which you couldn't possibly cut, but they could have any old shape. I think it was just an idealization [derived from] seeing metals that you couldn't do too much but that wear down. But as far as cosmology, I don't remember having too much of an idea, other than [about] the origin of the elements. I can vaguely remember reading some things about the big bang theory and the steady state theory, but it was rather dim.

Lightman:

You're not sure where you might have read something like that?

Page:

Right. I can't remember at what age I first thought about that.

Lightman:

Okay, tell me a little bit about your college experience.

Page:

I went to William Jewell College, which is a small, Christian, liberal arts college in the Midwest [Missouri]. It was the one that my parents had gone to, and some of my aunts lived in the area, so in some sense, it was more home than if I'd stayed within Alaska. If I'd gone to the University of Alaska, I would have had to live away from home anyway. For a college of that size — there were about 1000 people when I was there — they had a good physics department with three physics professors. One of them, Dr. Wallace Hilton, was a very energetic teacher. He didn't know an enormous amount of theoretical physics, but he did a lot with acoustics and optics and lab work and really encouraged people to do things. Later after I'd left, he won the Oersted medal as the top physics teacher of that year. I forget which year, but sometime when I was in graduate school, I think. So he was a great encouragement. He had programs of independent study and research, [giving] students one or two hours of credit just by spending Thursday afternoon working on something, on one's own. So he was a very enthusiastic teacher and would have signs around, like "Physics is fun." I suppose that by the time I went to college I thought I would eventually earn a master's degree. But I never particularly thought about going on for a Ph.D. Of course, at that stage I didn't really know what aptitude I had.

Lightman:

You weren't sure that you were going to go into science then?

Page:

Well, I was pretty sure that I was going into science. When I first went to William Jewell, I wasn't too sure whether it would be mathematics or physics. It turned out the physics department was quite a bit better there at that time.

Lightman:

I see. So that pushed you a little bit in the direction of physics?

Page:

That might have pushed me in [that direction], and I think my interests turned out to be more in [physics]. Looking back now, I can see that it was much better for me to go into physics, although [the physics I do] may be somewhat mathematical. But I'm not good at doing rigorous proofs or faking the style of pure mathematicians. Probably at the beginning of college I would not have realized whether my aptitudes were more in physics or math. At that stage, [the direction I chose] was probably more due to the better physics department there and just the encouragement that I got. And Dr. Hilton used to embarrass me by always referring to me as Dr. Page. That was his way of telling me I'd better go on and get a Ph.D., since I had not particularly expressed whether I would or not.

Lightman:

Did you learn anything new about cosmology as a college student?

Page:

One thing I do remember is that between my sophomore and junior year, NASA had a summer institute in space physics, held at Goddard Space Flight Center in New York, not too far from Columbia University. They had a five week program that I think about 30 of us [attended]. [There were] two or three courses for four or five weeks. Then the [last] week we flew around to the different NASA sites — Ames Lab in California and then down to JPL [Jet Propulsion Lab], across to the Houston Space Flight Center, and then to Cape Canaveral or Cape Kennedy, whichever the name was then, and then back to New York. So that was a good opportunity to get some input. We had courses on stellar structure, stellar atmospheres, and some astrophysics. I don't remember whether we had a course in cosmology per se. One of the physics professors at William Jewell, who came there after I'd been there one year, was C. Don Geilker. He had gotten a Ph.D. in astronomy, observational or mostly instrumental astronomy, but he gave me some guidance and helped to prepare me for this summer course. I didn't really have too much background, and most of the people were between junior and senior year, and [NASA] had somehow allowed me to go a year early. He encouraged me in that as well. Then I do remember in my senior year I read an article or two by Kip Thorne. That developed at least a little bit of interest in black holes before I came to Caltech, though I'm not sure that it engendered so much interest that I knew for certain that I would go into relativity.

Lightman:

It sounds like you had a little awareness of cosmology, but not very much at this stage.

Page:

Yes.

Lightman:

Were you aware of the different possible fates for the universe — the possibility of continued expansion versus a maximum expansion and then contraction?

Page:

It's hard for me to remember whether I knew of those possibilities. I'm sure I knew something about steady state and the big bang, but as to whether the universe would re-collapse, I don't recall having any thoughts about that.

Lightman:

Okay, we can pick that up later. I know that in graduate school at Caltech you more or less started in relativity, and even then you really didn't go into cosmology. Right?

Page:

Right. Yes, when I went to graduate school, at first I thought I was more interested in elementary particle physics. It was after I came to Caltech that I developed an interest in relativity. It's a little hard for me to remember precisely how early this was. I do remember that after the placement exams that we took early on, they had a party for us [new students] over at the [Caltech] Atheneum, and Kip Thorne was one of the relatively small number of professors who had enough interest to show up at this sort of thing. I remember having a nice conversation with him. I seem to remember I had a certain amount of interest [in relativity] after that, so maybe it was a turning point. It could also have been that I found particle physics somewhat confusing. I mean it was [such] a variety of information, and I didn't see such a clear pattern in that. I suppose another thing was that I did better in the relativity course than in the elementary particle physics course. So I had more of an interest of going into relativity and then basically started in [Kip's relativity] group after the first year candidacy exams.

Lightman:

You took Kip's relativity course, I guess.

Page:

Yes, I took that. I think Jim Gunn taught one semester [of it]. If I remember correctly, [in] the first term, Jim Gunn was teaching the relativity course while Kip Thorne was teaching a high energy astrophysics course. So, of course, that gave [me] a lot of interest. I don't know whether it was so much in astrophysics, but I certainly admired Kip's lecturing style and his clear expositions of things. And the relativity course became quite fascinating as well. Of course, you had to wait more or less until after finishing the first year and passing the candidacy exams before you really had a chance to get tied in with anyone anyway [as a thesis advisor]. So that didn't happen until that next summer. Well, there was also [another] thing. I had a low draft number, and I thought I was going to have to go into the military. I had searched out a Navy Medical Service Corps that I thought [might allow me to do] some physics for three years rather than two years in the infantry or whatever. So I got into that program after my undergraduate degree, and they were going to give me up to two years to finish my next degree. It looked like I was going to be able to finish the master's degree in the first year, which I thought would be better. Then I could go in [the Navy] and then come back. I wrote to them and said I was going to finish that year and [asked if they] would like me to stay on for a Ph.D. They wrote back, and they didn't have any objections to my staying on and doing a Ph.D. first — which was quite fortunate because Kip said I would have gotten quite rusty if I had gone out for three years, even though I'd been doing some physics. So it turned out very lucky. Then, by the time I finished my Ph.D., the Vietnam War was over, and the draft was over, and even though I had made a commitment to go in the [Navy], they let me out of it. They said if I didn't want to come, I didn't have to. So I didn't get my career interrupted by the military service after all.

Lightman:

Yes. I had been in the same situation the previous year (1969-1970), when I was a senior in college. I had been exposed to the lottery, but I happened to get a high number, so I was never real worried about it.

Page:

Yes. I was sufficiently upset at the lottery that I did a whole statistical study of it and found that the correlation between the date and number of the year was about four and a quarter standard deviations away from what you'd expect. Which was quite naturally explained by the fact that they dumped the capsules into the box one month at a time, presumably with December being the end, and then turned the box over several times and pulled them out. So with December 31st as my birthdate, it was a little bit more probable. The mean number for December was 121 or something.

Lightman:

Before we leave graduate school, let me ask you this. When you took the relativity course - I took the same course, and there was a big section on cosmology, in which all of the various models were discussed in some detail — do you remember at that time having a preference for any particular cosmological model, like open versus closed?

Page:

I don't remember an enormous preference. I know, of course, at Caltech there seemed to be more emphasis on the observations, which at that time seemed to favor an open universe.

Lightman:

And still do.

Page:

[Laughs] That's true. They still do. The case for a closed universe ... it didn't seem like one knew of matter density more than maybe omega of 0.06, or whatever it was at that time. I can remember that I took Willy Fowler's 8AM course on nucleosynthesis and nuclear astrophysics. I can remember at one stage he said that according to the Caltech religion, the universe is open, and according to the Princeton superstition, it's closed. I suppose I inherited a bit of that feeling of going with the observations more. I know, of course, that the Misner, Thorne, and Wheeler book^[2] — some parts of the cosmology having been apparently written by Wheeler — strongly favored the closed universe. But I don't know that I had any strong prejudice. I suppose just by listening to what the observational results were and the lack of evidence of other matter, I thought that it was more likely that the universe was open. But that was more a function, I think, of what I was hearing at the time rather than any particular prejudice on my own part.

Lightman:

Could you tell me how it was that you started working in cosmology, from the time that you finished up your thesis, which was not on cosmology as I remember?

Page:

Yes, I suppose it was, in a sense, a long route. After the first year I started with Kip, that summer I asked him whether he had some good problems with black holes, and he thought that so many people were working on black holes, maybe I should work on something else. He gave me some problems with the cylindrical universe, which I wasn't really getting anywhere with. Then I became interested in this superradiance that Saul Teukolsky and Bill Press were doing a lot of work on.^[3] I was trying to figure out how one would describe that quantum mechanically. It took me a while just to realize that it was simply stimulated emission. After realizing that, it occurred to me that there ought to be spontaneous emission. I remember we managed to get [Richard] Feynman to come over "to Bridge Lab, and we [wanted] to explain this to him and see if it made sense to him. He came over, and he wanted to have a model for black holes with little vanes sticking out or something, so he could have a physical model for how these rotating black holes can amplify waves. I remember I was there, and Saul Teukolsky and I think Doug Eardley was there at that time as a post-doc, and you and Bill Press.

Lightman:

I remember those conversations.

Page:

Yes, I remember it was a lot of fun, because after we more or less convincing [Feynman] that there should be this application, then I think Saul Teukolsky asked him why the neutrino waves weren't amplified. Saul had just separated the equations for neutrinos [scattering off black holes], and he'd found that they weren't amplified. He asked Feynman why that might be. I remember Feynman quickly understood this, and realized it was basically an exclusion principle — you couldn't get more than one neutrino in a state so if you sent one in, you couldn't get more than one out. I do remember an amusing situation. When [Feynman] was at the black board he was trying to draw some neutrinos going in, antineutrinos going out, and he was trying to figure this out at the blackboard. He wasn't too sure of exactly how to write that down. And he said, "I'm supposed to be good at these diagrams." But it was a lot of fun. [Feynman] had such willingness to talk to even green graduate students about this.

Lightman:

He used to go to lunch with us, didn't he?

Page:

Yes, yes.

Lightman:

Every couple of months or so.

Page:

Right.

Lightman:

So this got you involved with putting quantum mechanics and relativity together, in a way?

Page:

Yes. I remember that a couple hours after Feynman left, I was trying to find some way to calculate this [spontaneous] emission. I discovered that Zeldovich and Starobinsky had a paper^[4] [in which] they had a two line statement saying that when they had predicted the stimulated emission, or amplification, they also predicted the spontaneous emission. Of course, I was a bit crestfallen that someone else had already predicted this effect. But I got interested in calculating it, but I didn't really know how to do it formally. Then Stephen Hawking indirectly, I think, heard of some of this stuff through Doug Eardley, who had told [Hawking] that I was working on some of this. Then [Hawking] had a chance to talk to Zel'dovich and Starobinsky in Moscow. He liked their idea but didn't like their derivation. So he sat down to do it himself and, 10 and behold, he found that there was not only spontaneous emission of these amplified modes, but all modes produced particles. This was very surprising to him. So this was his famous Hawking radiation.^[5] Then we, of course, heard of this at Caltech and got his preprint and at first it was a little hard to know whether we believed it or not. So then I began doing some numerical calculations. When Stephen Hawking spent the year 1974-1975 at Caltech as a Fairchild Scholar, I got to know him. We ended up writing a paper^[6] proposing that people look for gamma ray bursts from primordial black holes that might be exploding. Then I finished my thesis on calculating numerical rates of particles coming out from rotating and non-rotating black holes.^[7]

Lightman:

So this was the start of your association with Hawking.

Page:

Right. In my last year, 1975-76, I was applying for a number of post-doctoral opportunities. Of course, I had Stephen Hawking as one of my references. Then he wrote me at some stage and said, "I've been writing letters of reference for you, but I may have a position myself." Gary Gibbons, whom he had been supporting, was invited to go to Munich for a year. So that opened up a one year position in Cambridge. I went there in 1979 and was a post-doc. Then Stephen Hawking got support for two more years, although, in one of those years, actually I got some [of my own] support from a NATO fellowship. So I was in Cambridge from 1976 to 1979. By then Stephen Hawking was interested in doing this Euclidean quantum gravity with instantons. I did some calculations of gravitational instantons at that time.

Lightman:

Can you tell me briefly what an instanton is?

Page:

An instanton is a solution of the gravitational field equations with what Hawking calls Euclidean signature. That is, all four dimensions have the same character as space. Essentially, if you just took flat space time and made time imaginary, then the metric would be positive definite. There are various other examples. One simple example would be a four-sphere.

Lightman:

What is that physically supposed to correspond to?

Page:

The full meaning of [instantons] has always been somewhat uncertain, but the hope is that [instantons] would be [make] dominant contributions in a path integral. If you try to quantize gravity by the Feynman path integral technique — for example, if you want to calculate transition amplitudes, you go from one three geometry to another — then you would fill in with all possible four geometries and then for each one you'd have an action.

Lightman:

Right.

Page:

Normally, if you [calculated] with a Lorentzian signature, you'd multiply the action by i and divide it by h, exponentiate, and sum this up over all the configurations.

Lightman:

What's wrong with doing it that way?

Page:

If you do it with Lorentzian, first of all, you have an oscillating integral, and it's not too well behaved. One hope for getting a better convergence [in the] path integral is to go to Euclidean. Then the action becomes imaginary, and [multiplying it by i] gives an [exponential with a real argument]. So if the action's positive, then you'll get a damping and you can hope [the sum will converge.] Now with gravity, it turns out there's a problem because the action is actually not positive definite. It can be negative because of conformal modes. If you scale the four-dimensional metric and then interpolate between the two 3-metrics you're interested in, by some factor that varies from place to place, you can get the action to be arbitrarily negative. Gary Gibbons and Stephen Hawking and Malcolm Perry made some suggestions^[8] for how to get around that. It's not too certain how to do it. In fact that [problem] even arose out of discussion just today with Sidney Coleman. He said, "How do you handle this conformal factor?"

Lightman:

Well, I shouldn't have gotten you off on this slight digression of instantons. You started working with Hawking on path integral formulations of cosmology or quantum gravity.

Page:

Right, at that time, I suppose it was quantum gravity more than cosmology. We hoped that these [instantons] might dominate, that they might act as stationary phase points. Then, after going to Penn State, after getting an assistant professorship which eventually became tenured at Penn State, I worked a little more on that, but I had a variety of interests. One thing that occurred after I got back [to the U.S.] related to Stephen Hawking's proposal that black holes might cause a loss of information from this universe. You could have particles going into the black hole, [carrying information], but then the black hole emission — if it's purely thermal — would lead to a pure state going into a density matrix. After getting away from Cambridge, I began having questions [about] how firmly this was proved, and so I wrote a short paper^[9] for Phys. Rev. Letters questioning whether that was necessarily the case. Basically, Stephen Hawking and I [have] kind of debated that ever since. I don't know that either of us has come up with terribly strong arguments. Stephen has come up with more arguments than I have, more or less for loss of quantum coherence. Although recently I think he has begun to become somewhat convinced that you don't lose this quantum coherence on a very small scale, for little virtual black holes, [as argued by Sidney Coleman]. I was working more with black hole thermodynamics and various problems of quantum gravity until Stephen Hawking proposed the idea for the boundary conditions of the universe, at this meeting in the Vatican, I think in October 1981.^[10] Then, in the next year, he and James Hartle worked out the mathematical details, which they published^[11] in 1983 Physical Review. I had a great amount of interest in that because I realized that one needs a lot more than just dynamical equations in physics; one also needs to have boundary conditions, particularly to explain such things as the second law of thermodynamics. It's not something that one can derive purely by laws as we know them. The dynamical laws as we know them are CPT invariant. So it would seem very difficult to get an arrow of time directly out of those dynamical laws. Maybe the new boundary conditions could help.

Lightman:

In this case the boundary conditions [should show] why the universe started off in a state of very low entropy.

Page:

Right.

Lightman:

Then it just reduces to probability arguments. Once you've started off in an improbable state, then just the [evolution] towards a more probable state increases entropy. So that's really what you mean, in some sense, isn't it?

Page:

Yes. I mean just to try to get some sort of explanation [of why] the universe seemed to have very low entropy when it started.

Lightman:

Were you thinking in terms of a beginning [of the universe]?

Page:

I've had a lot of interest in the second law of thermodynamics and .the arrow of tirp.e - partly arising, I suppose, out of black hole thermodynamics and entropy. So I knew that there was this problem of the arrow of time, even before Hartle and Hawking made their proposal. I can remember that Paul Davies had argued that perhaps inflationary universes might explain the arrow by winding up the gravitational field, although I was never completely convinced that he had explained it. It seemed that inflation assumed that you had a second law of thermodynamics. We had a bit of debate with a couple of articles in Nature. He had a paper,^[12] and then I had one.^[13] Then he had another one,^[14] and then I think later at some other conference proceeding, [I had something else] on that.^[15] So I was somewhat interested in entropy in the early universe, even before the Hawking proposal. These amazing facts about the universe — that it's so highly ordered, with very low entropy at the beginning, as well as its isotropy and homogeneity — seemed to impress [upon] me that one does need more than just dynamical laws. Therefore this Hartle/Hawking proposal had a great deal of appeal to me, and I perhaps [felt] like defending it even before other people did. I can remember at a conference — I think this was in December 1982, at one of the Texas relativity conferences — there was a small meeting of some relativists up at the University of Texas one day. Stephen Hawking was actually at the Texas meeting, but I think he was doing some work with Ian Moss on inflation that particular day, so he wasn't there. James Hartle was explaining this "no-boundary proposal" that they were making. [He was] doing the math of it, but at that stage he wasn't wanting to defend the philosophy of it. I remember [thinking that] if this idea is correct — of course, you couldn't be sure whether it was correct — it was a sufficiently important idea that maybe I should defend the philosophy of it. So I was speaking up on that...

Lightman:

How would you defend the philosophy of it?

Page:

Well, I was just saying that one needs something to specify the [initial] state of the universe. In physics, we wouldn't have a complete description until we had something like that.

Lightman:

Some people might" just be willing to accept initial conditions [as givens].

Page:

Right. I remember when I said this that Bryce DeWitt immediately popped up and he said, "You don't want to give God any freedom at all." So before I could think of an answer to that, then Karol Kuchar said, "That's His choice. And I imagine that he meant that it's not really restricting God's freedom by finding out what laws He may have used..."

Lightman:

Well, would you agree with Kuchar on that?

Page:

Yes, I think very much that I would agree. I am a Christian and believe that God has created the whole universe. Of course, as a physicist I'm trying to understand a bit more of how He did create it or in what state He's created it. But I think these laws show the faithfulness of God and the patterns that He's used. On the other hand, I don't think the laws are constraints on Him. It's his own choice to create with these things. You could say, of course, after having made the choice, God sticks to this choice. Then you could say, "Maybe He doesn't have the freedom that He used to," but of course, that's true with any being that makes choices. Once you've made the choice, then in some sense you've restricted your freedom. But I don't believe at all that these choices were forced upon God by anything — it's hard to say anything external. Einstein [said] that the question he was interested in was whether or not God had any freedom or any choice in creating the universe. And it seems to me that you could never prove that He didn't have some choice, although I know a lot of physicists do think or seem to have the hope that there might only be one consistent theory for the universe.

Lightman:

Do you think that there is only one consistent theory of the universe — that the universe can have only one set of [physical laws], that it can be only ten dimensions or four dimensions or whatever the number is, that the speed of light can have only the value it now has, and so forth? Do you believe that?

Page:

No, I think [the universe] could be vastly different. I can imagine all sorts of ways [in which] it could be different. In fact, I think when most of these people say that there might be only one consistent theory, I think what they mean is only one fairly simple theory that might be consistent. For example, if you're going to say that the universe is governed by quantum mechanics in some specific Lagrangian, perhaps in some quantum form, if it all comes from one single equation, which would be a big restriction. But, logically, it seems to me that one could have a whole lot of variation. You could say that it's a big mystery why [the universe] should be described by one set of equations. Why couldn't God do something entirely different here from there? In principle, the whole thing could be quite different. Now I don't know why He's chosen to follow these laws. I suppose, of course, if [the universe] were completely chaotic, it would be hard for any intelligent beings to be created within it, and it would be very hard for [the universe] to have any order. On the other hand, [the universe] does seem to have a lot more order than would be necessary merely for our existence. So why God has chosen to make it even much more ordered than we might have needed...

Lightman:

Is that something you think you can discover by understanding the initial conditions?

Page:

Well, there are two parts to the order. There's the part in the dynamical laws, which you might say [derive] from the Lagrangian. Then there's the part in the initial conditions.

Lightman:

And I gather that you're putting those on the same footing, in some sense. You're saying that they're both part of physics.

Page:

Right. Or that they could be. Now, it's certainly logically conceivable that God may have put an enormous amount of order in the dynamical laws. If you use a picture of things evolving — although that maybe a questionable description of quantum gravity — then you could say that the dynamical laws put an enormous correlation, or maybe a rigid correlation, between what happens at one time and what happens at another time. Suppose God created an angel that was sufficiently intelligent to understand the laws and be able to carry out the calculations of how the universe would evolve under these laws. Then if God told this angel these laws and He told him the initial state of the universe, then this angel should be able in principle to calculate the state of the universe at all other times. So that's what the dynamical laws do. But, of course, those [dynamical laws] by themselves, [without the initial conditions], would not say what state the universe would have to have at anyone of these times.

Lightman:

No.

Page:

So the dynamical laws give the correlations between the different times. But it's logically possible, of course, that the initial conditions might not have a simple description. Then it's a choice of words as to whether you say [the initial conditions] are random or not. If the initial conditions were random, it would mean that there would be no simple description of them. And one gets into a bit of a tension if one tries to psychologically describe these things [in terms of] which is better, from a human point of view. There's one part of people's psyche, or my own psyche, that says it's better if God put an enormous amount of information in the world. If the universe is really as simple as that described by some Lagrangian and some particular boundary condition, such as the Hartle-Hawking boundary condition, then it seems like God didn't really put an enormous amount of information in the universe. You might think, well, maybe He should have put in more information. On the other hand, a high amount of information is, in a certain sense, equivalent to a high amount of randomness. That is, if it's something we can't predict, then you can say it's random. So one could always be torn between wanting it to be either more random or more simple. The second law of thermodynamics seems to indicate that there's a certain amount of simplicity in the initial conditions. There must be. Whether it's as simple as the Hartle-Hawking proposal, of course, we don't know.

Lightman:

Simplicity in the sense of a lot of order?

Page:

Right. And also in the sense that one could try to describe it. Some people do computer complexity theory and so on and can talk about how much information there is in something by the shortest program that you could write that could specify it. Now, it's very hard for me to see how you could actually quantify [information] for the state of the universe. Even if superstring theory turned out to be the ultimate physical theory, with the Hartle-Hawking boundary conditions, I don't know how you'd quantify how many bits of information are in that description. The Lagrangian might not have too many bits [of information], but there's a whole lot of assumed background to what all these terms mean, what a Lagrangian means. I don't know how you would specify that. I think there does seem to be a lot of evidence that the universe is a lot simpler than what it conceivably could be.

Lightman:

Consistent with the fact that we're here. That's what you said earlier.

Page:

Right. Consistent with the fact that we're here. Yes, I suppose that's always a constraint. At the moment, I was even saying I could allow all conceivable possibilities whether or not they allow life. Of course, we know if [the universe] were so chaotic that people couldn't be here, then we couldn't be here to ask the question. But I do believe the weak anthropic principle leaves us a useful guide. I think one shouldn't spend too much time bashing one's head and trying to explain where we are within the universe or which sort of sub-universe we're in, if there are many different [universes]. People talk about many universes in different senses.

Lightman:

In your program in quantum cosmology, when you're doing these path integrals over lots of different 3-geometries, isn't it true that you can interpret that [operation] as the consideration of many different universes, each with a probability amplitude?

Page:

Right. Yes, I think in a sense when you do the path integral you get non-zero amplitudes for a whole lot of different possible situations.

Lightman:

Isn't it true that, depending on whether you take the Copenhagen interpretation of quantum mechanics or the many-worlds interpretation, you could possibly think of all of these universes as existing, or at least having the probability of existing?

Page:

Yes. I myself probably hold more to the Everett interpretation, or what's usually called the many-worlds interpretation.

Lightman:

So you would say that these many different universes are actually all simultaneously existing in some sense.

Page:

Right. I think I would. It's partly on the grounds of simplicity that I don't want to have to add extra elements to quantum mechanics for the collapse [of the wave function]. So it seems very likely that this grand wave function — even though it might be rather simple in the sense that you could specify it by path integral with no boundary — would be a superposition of an enormous number of terms if you decomposed it into eigenstates of some macroscopic operator.

Lightman:

Earlier you said that you felt that God created the universe, and whichever way He created it was a way that He chose to create it. If you now try to reconcile that viewpoint with this many worlds interpretation of quantum mechanics — in which all of these different universes, possibly with very different properties, are existing simultaneously — would you then say that God created all of these different universes?

Page:

Yes, I would say He's creating all of these different universes. I almost thought you were going to say that if the many worlds picture is correct, then all these possibilities existed and therefore God created everything and there's not really a choice. Well, I don't know. The many worlds [view] doesn't necessarily mean that all possible worlds exist in the wave function. There could be a lot of possibilities that have zero amplitude. I suppose maybe more strictly, they have varying amplitudes. The different components would have varying amplitudes. Usually, you associate the absolute square of an amplitude with probabilities. I would prefer to interpret the [amplitudes] as just being some measure on the things. In some sense, some worlds exist with a higher measure, which is normally what you would interpret as probability. But if I say they're actually existing, it's a little hard to say, in an ontological sense, that one has more probability than the other.

Lightman:

To translate the measure into something meaningful, you need to have a huge ensemble of universes and to say which fraction of them are like this universe, and which fraction are like another universe, and so on — which is a boggling concept, at least to me anyway.

Page:

Yes. I suppose in a sense the Everett interpretation says that quantum mechanics provides its own ensemble. It's saying that all these possibilities exist. But it is a somewhat strange ensemble in that the number of elements in the ensemble depends on how you decompose the wave function. You could always just say it's one wave function, and then you've just got one component. So it depends on your basis [functions], and it's not at all the same as a classical ensemble. You have the freedom of choosing your basis. But if you do chose a specific basis — for example, if I chose a basis in which there were certain eigenstates of this basis in which I existed — then if a simple proposal for the universe is right, I would think that my eigenstates would only be an enormously small fraction of these components.

Lightman:

Before we leave this point, which is very interesting to me, if we imagine that there is this large range of universes that all simultaneously exist, do you think there's anything other than the anthropic principle that would make universes with life special?

Page:

Well, let's see. Of course, the weak anthropic principle is in a sense saying that our observations have to be consistent with life.

Lightman:

Right, but what I'm asking you now to do is to take a step back — to look at the whole ensemble and not just look from the point of view of our particular universe.

Page:

Right. So I imagine myself outside of [our universe], which I do all the time. I imagine myself outside of it, just thinking about the whole ensemble. So I'm not restricted to looking at just those components [universes] in which life exists.

Lightman:

No, and presumably you're also thinking this way when you do your path integrals. You're stepping outside. I guess this is getting back to your belief in the Creator, which you can comment on or not.

Page:

I suppose God might be more interested in those components in which there is life, although I'm not quite sure how r would put that in operational terms.

Lightman:

You mean quantize that. [Laughs]

Page:

I guess it's a question of how would I say that he's more interested in [universes with life]. I don't know. It's an interesting thing. I'm a pretty conservative Christian in the sense of pretty much taking the Bible seriously for what it says. Of course, I know that certain parts are not intended to be read literally, so I'm not precisely a literalist. But I try to believe in the meaning that I think it is intended to have there. I do know also that a lot of Christians believe that man is the main purpose for God's creating the universe, but I'm perhaps a little less certain of that than many of friends are. I do know that the Bible reports that God created man in His own image, but whether that means [man is] uniquely in His image, whether He could have created some other beings somewhere else that are in His image but quite different [from man], I don't know. Maybe [God] even created some things that aren't life that might be said to be in His image. I don't know. The Bible doesn't really say much about that. I think the main point of the Bible is how He created man in His image, and man fell and rebelled against God, and then God offered the way back through Christ and Christ's death on the cross. I think probably it focuses mainly on man's relationship with God, without attempting to answer the questions of what other purposes God may have had in creating the universe. So I am a bit skeptical about applying the strong anthropic principle, that the universe had to have life in it, or [life] was one of the necessary purposes for God to create the universe. Well, He did choose to create a universe that does have life in it, or at least in the component of the wave function in which we exist, but I'm a little bit hesitant to say that that was necessarily God's only or even God's main purpose for creating the universe. He might have a lot of other purposes that we don't know. I certainly don't want to deny that [life] was one of God's purposes. Maybe it's the main one that's focused on in the Bible — man's relationship to God and so on. But I don't think the Bible's intended to answer questions about everything that God did, and how He might have created something else that we know nothing about.

Lightman:

Do you think that the universe has a purpose? Let me ask that in the context of a very interesting quote that Steven Weinberg makes in his book, The First Three Minutes, which you might have read. Weinberg says that the more the universe seems comprehensible, the more it also seems pointless.^[16]

Page:

Yes, now I would say that there's definitely a purpose. I don't know what all of the purposes are, but I think one of them was for God to create man to have fellowship with God. I suppose a bigger purpose maybe was that God's creation would glorify God. It talks in the New Testament about all creation being created through Christ and by Christ and for God's glory. So I think that's at least one of the purposes. I'm just a little reluctant to say whether that's God's only purpose. Maybe I should say that I do believe the Bible is God's revealed word to us, so I think that's one purpose that has been revealed to us. Other purposes we could just try to guess from some other means. We see such mathematical beauty and simplicity and elegance in the physical universe, in the dynamical equations that God's created here. I'm not quite sure how to tie those aspects of the creation into purpose. In some sense, [the physical laws] seem to be analogous to the grammar and the language that God chose to use. The purpose seems to relate more to other aspects of what is created. [It's] a bit like if you tried to analyze the grammatical structure and so on of some of Shakespeare's writing, but you didn't at all look at what the plays meant, or what the story was there. There can be these different descriptions on different levels.

Lightman:

That's a beautiful analogy. I think I've steered you far enough into this territory. Maybe I'll retreat back into some specific scientific issues, although all of this might be looked at in the larger context. I did want to ask you a couple of specific things about your reactions to some discoveries that have happened in the last ten or fifteen years.

Page:

Okay.

Lightman:

Do you remember when you first heard about the horizon problem?

Page:

It's hard for me to remember when I first [heard about it]. To be honest, I'm not sure that I do remember precisely when I heard that.

Lightman:

Did you know about it when you got the cosmology unit at Caltech? Was it discussed then?

Page:

I don't really remember it's being discussed then. I think it must have been sometime when I was doing research or something and I read something about it. It might have been mentioned, but I don't really remember it sinking in.

Lightman:

So maybe sometime in the middle 1970s or by the late 1970s?

Page:

Yes, probably. It was probably after course work. I don't remember really thinking about it too much when I was at Caltech. I must have known of it then, but I'm not even sure I thought much about it.

Lightman:

When you did think about it, whenever that was, late 1970s or whenever, do you remember whether you regarded it as a serious problem?

Page:

I suppose it emphasized the problem of the homogeneity and isotropy. I guess I've always been a bit skeptical as to whether the horizon problem is a separate problem.

Lightman:

Yes, the homogeneity [problem], that's what I mean by horizon problem: the fact that we see regions of the universe that appear to have exchanged information and homogenized and yet are so far apart that they couldn't have done so in the time since the big bang, according to the standard model. Did you regard that as a serious [problem]?

Page:

Yes. I don't remember when I first heard of that aspect of the problem the causal disconnection at early times, but yes, I thought that that was a serious problem. I do remember one time — it was pre-inflation — I had dinner or breakfast or something at some meeting with Bill Press. I remember he made the remark that homogeneity and isotropies were not so hard to explain. You just have to say that the situation [at early times] was smooth. You use one word. So he was emphasizing that the real problem was to get the fluctuations for galaxies. Now, in a sense, [he] was taking more of the attitude that there was something — he didn't say what it was then — analogous the Hartle-Hawking proposal that would [involve] some special initial conditions.

Lightman:

Yes, that's what I wanted to know. Did you personally think that the resolution of this horizon problem, or large-scale homogeneity, might lie with the initial conditions?

Page:

Yes, once I thought about it. I suppose when I first took the courses and heard the problems; I don't know that I thought of it. But yes, I certainly came to realize that. That would be something for the initial conditions to explain.

Lightman:

Were you' willing to just accept initial conditions that had this property?

Page:

I suppose I thought that it ought to come out of something fairly natural. I'm not quite sure what. A lot of these things were influenced by Roger Penrose's calculations^[17] of the entropy if [the entire universe were] an enormous black hole. If you took all of the particles in the [observable] universe and put their rest mass all into a big black holes until the mass is roughly the sum of the rest mass of these particles, then you'd have a black hole [with] a mass of...

Lightman:

10²² solar masses. Something like that.

Page:

Yes, 10²² solar masses, which is about 10⁶¹ Planck units. So it would have an entropy of around 10¹²³. Penrose emphasized that the numbers of states is roughly the exponential of the entropy, so you'd have e¹⁰¹²³ states, which is just an utterly enormous number, even compared to, say e¹⁰⁹⁰, if you had 10⁹⁰ photons in the observable universe. Although one might question some of the assumptions of such a calculation, such as fixing the energy and putting it all in a black hole and so on, Penrose's emphasis was on how special the initial conditions of the universe were. You get enormously big numbers for the possible entropy if the universe were in some different configuration that had a lot of gravitational entropy. Before some of these calculations, it was always a little bit confusing because of the fact that the early universe was rather hot and uniform and, locally, it was fairly near thermodynamic equilibrium. With non-gravitational systems, thermal equilibrium tends to be a state of high entropy. So in that way of looking at it, you'd tend to think that the early universe had high entropy. So Penrose is probably the main one who got me to see that [the entropy of the early universe really] wasn't that high, because the gravitational field was quite smooth.

Lightman:

Compared to what it could have been. That's where the missing entropy is.

Page:

Right. So I felt that one needed to have some explanation for that. And admittedly, I wasn't quite as much convinced that inflation solved this problem as a lot of other people were.

Lightman:

I was going to ask you about that.

Page:

Maybe by the time inflation came around, I realized that this second law of thermodynamics [question] seemed to be a more special problem than just the homogeneity and isotropy. Those were special aspects, but these numbers that Penrose got from thermodynamic arguments were so huge. I don't know exactly how to quantify the homogeneity and isotropy. I'm sure they must be extremely special, too, but probably not as special as the second law. Although, of course, you could say we really don't know that the second law applies for sure for such long ways away from our past light cone. The stars that we can see all seem to be more or less obeying the second law, as far as we can tell. So it seemed to me that [special, low entropy initial conditions were required] even to have inflation, even to start off with a somewhat lumpy universe but have inflation cause the thing to expand by a huge factor.

Lightman:

You mean you would have to have a direction of time already defined. Is that what you mean?

Page:

Right. Yes, I think that in fact gets back to these arguments that I was having with Paul Davies. Paul Davies was arguing that you could then wind up the universe or wind up the clock of the universe [and] get it into a state of low gravitational entropy by having inflation, whereas it seemed to me that you would have to have low entropy even to have this inflation.

Lightman:

I see. So you felt like the inflation didn't really solve this problem, because there was a more fundamental problem that needed to be solved prior to inflation.

Page:

Right.

Lightman:

That's very interesting.

Page:

Yes, I thought that the homogeneity and isotropy might come as a consequence of whatever it was that solved this bigger problem of the second law of thermodynamics.

Lightman:

That's very interesting. Did you regard the inflationary model as being a big success in some ways?

Page:

I perhaps reacted a little bit negatively towards it because some people made what seemed to me slightly exaggerated claims about what [the inflationary universe model] solved. Alan Guth has really been quite fair about it in not making too many exaggerated claims. I was thinking that some of the problems [inflation] attempted to solve could be solved by some other means. It didn't seem to me that [the inflationary model] solved the [problem of the] second law of thermodynamics. [And if you could solve that latter problem], I was trying to think of some alternate ways that you could get the isotropy and homogeneity out. I have some hand-wavy, crazy argument that in quantum gravity, because the state has to be invariant under shifting the whole position, the only way you can get structure in the gravitational field is to have correlations. It would seem to me that one way of describing the second law of thermodynamics is to say that the early state of the universe lacked long-range spatial correlations. In some ways, that's one way to describe the second law. Things start off uncorrelated, and then relationships develop and correlations develop. It's sort of the same process that we have when we learn about ‘if...' things. I mean, we're becoming correlated with things. In some sense, we're learning more and more about less and less.

Lightman:

Yes, but as we're learning things we're increasing the total entropy [of the universe] in order to learn.

Page:

Yes, it's all in some sense part of the same thing. It's a little paradoxical how you describe it.

Lightman:

Yes, it depends where you draw the box around the system.

Page:

Growing correlations.

Lightman:

You have to lose correlations somewhere else to grow them in one place, don't you?

Page:

What I mean is I'm developing correlations between what's here locally that I have access to and something that's gone way out over there. And because I don't have access to the correlations anymore, that information is lost. If the early universe started off uncorrelated, then essentially all the information was in the local regions, because there wasn't information in the correlations between the regions. But then as correlations develop between parts of the universe that are far apart, if you don't have access to the correlations — if you can only have access to the local information — then the information you have access to is less than what there was before. If the universe evolved according to some deterministic fashion, then the information is never really lost, but it can go into these correlations that you don't have access to. So I tended to like that description of the second law, which is basically a quantum version of the version that Percival and I think Oliver or Penrose^[18] formulated — conditional independence or something. So I thought the second law you'd need to explain, and inflation didn't explain that. And I thought if you did have a second law then you could perhaps explain the homogeneity and isotropy. I wasn't too sure. The monopole problem was something that was [explained well] by inflation. I did work^[19] with [Vigdor] Teplitz and Duane Dicus.

Lightman:

What's [Teplitz's] first name?

Page:

Let's see, was it Vigdor?

Lightman:

This was a collaborator of yours, and you're having trouble remembering his name? [laughter] I forgot some of my collaborators, too.

Page:

Well, I ate too much tonight. Anyway, this was largely a long-distance collaboration. Teplitz and Dicus had written some stuff about monopole annihilation, and then I had done this crazy calculation^[20] for the future of the universe. I remember that you invited me to Harvard to give a talk about [that work] several years ago. We found that the main mechanism of getting rid of electrons and positrons in the distant universe was three-body annihilation. Three [particles] would come in, and then one of them would carry off the excess energy so the other two wound up in a bound state. I remember we were going to look and see if that could help get rid of monopoles in the early universe. It turned out to be a rather more effective method of getting rid of monopoles, but we couldn't get it to work to get rid of enough monopoles.

Lightman:

So inflation's really solved this problem.

Page:

So it seemed to me that inflation solved that problem, although I was slightly reluctant... I had some secret hope that maybe we could find some other solution to that problem. But it did seem that [inflation] solved [the monopole] problem. Now I believe that inflation is certainly a part of the evolution of the [universe]. I mean, it seems to be likely to have been part of the past history [of the universe].

Lightman:

Because it's come 'out of quantum cosmology.

Page:

Yes. I still have some resistance [to inflation]. I've even been doing some classical calculations. People talk about how probable inflation is. I was doing some calculations^[21] with Stephen Hawking, and then on my own,^[22] using a certain classical probability measure that Gary Gibbons and Stephen Hawking and John Stewart^[23] developed and also Mark Hanneaux,^[24] independently and actually earlier. I found with just this classical measure, which is not quantum mechanical, which you can try to calculate with some very simple models what the probability of inflation is. It turns out to be unambiguously ambiguous. That is to say, the measure of inflationary solutions is infinite, but so is the measure of non-inflationary solutions. You can take the ratio any way you want, and in fact we have some explicit ways of getting high probabilities of inflation, and other ways of getting low probabilities.

Lightman:

Why do you think the inflationary model caught on so widely?

Page:

I suppose that it does seem to solve some of these problems. Maybe I've been a little bit too much prejudiced against it. Maybe I've overreacted to some of the extreme claims for it, but it does provide a mechanism for making the universe large and fairly smooth. And it does provide a mechanism for amplifying some small quantum fluctuations into larger fluctuations that might be able to turn into galaxies and so on. Although even there you have to assume that these small perturbations start off near the ground state, which is something that can be justified by the Hartle-Hawking scheme modulo all the difficulties of really doing quantum gravity. Then, of course, it was another [model] that combined particle physics and high-energy physics with cosmology. So perhaps a growing overlap there. I mean, Alan Guth started off in particle physics, and then he [realized] that some of the results there could have impact in cosmology. So I really shouldn't decry [the inflationary universe model]. It is certainly a very important development. By the time inflation came out, Roger Penrose's arguments about all the entropy had caught my mind, and the second law of thermodynamics seemed to be a much bigger problem. Maybe the fact that I didn't think inflation solved that problem made me think it wasn't the solution of everything. But it's certainly an important contribution.

Lightman:

Another problem that the inflationary models are purported to solve is the flatness problem, which could be stated in many different ways. But one way of stating it is that the ratio of kinetic to potential energy at the Planck time [was so nearly close to one].

Page:

Right. Or, as I sometimes say it, why has the universe has grown so big and yet gravity's still important. I mean [gravity's] still slowing things down.

Lightman:

Yes, right. And omega's not 10^-25 or something.

Page:

Right.

Lightman:

Do you feel the same way about the flatness problem — that it is one of those problems whose solution will come out of a pre-inflation period?

Page:

I suppose I think [the flatness problem] is something that inflation could well solve. I never did consider that to be as important as the homogeneity and isotropy.

Lightman:

Why is that?

Page:

I suppose just because it's one number. I mean it's true that it's one number that's very finely tuned. Say, at the Planck time, this balance was to one part to roughly 10⁶⁰ or maybe 10⁵⁷, whatever it is. So you might say that's extremely improbable, getting one chance in ten to the sixty, but then [with] these other things that Penrose argued, you're one chance in e¹⁰¹²³. It's extremely much less probable that you'd have a second law of thermodynamics. It would be very hard to quantify, and actually I think the first attempt at this was Steven Weinberg's paper^[25] within the last year or so, on whether the anthropic principle implied something [like] this. I had a bit of impression that well, if the universe recollapsed much before now, there just wouldn't have been time for life. On the other hand, if it was open...

Lightman:

If it were too open, you wouldn't have formed bound structures.

Page:

Yes, it wouldn't have formed matter, that's right. I'm really getting more confused. I'm more confused on the cosmological constant.

Lightman:

Weinberg's paper was on the cosmological constant.

Page:

Right. So the flatness problem, so I suppose it's still...

Lightman:

It's not unrelated.

Page:

Yes, they're sort of tied together. Maybe I thought the anthropic principle might be sufficient for the flatness problem. It would depend on your a priori probabilities. I thought it was conceivable for that, whereas I did seem to recognize that it'd be very hard for the anthropic principle to explain the isotropy and homogeneity, because why would your existence depend on something way off somewhere else, that we are just now beginning to see, that could not have influenced [us] at all before [now].

Lightman:

When did you first hear about the flatness problem? Was that later than the horizon problem?

Page:

Probably earlier, but I'm not sure. Wait a minute. Who's the guy at Jodrell Bank, the popular radio astronomer.

Lightman:

Not Martin Ryle?

Page:

No, he did a lot of popularization. [Sir Bernard Lovell]. I think he wrote something about how precisely was this balance between [kinetic and gravitational energy]. Of course, it also came out in the Einstein Centenary Volume.^[26]

Lightman:

Robert Dicke and James Peeble talked about then. Was that the first time you heard about it? That was in 1979.

Page:

I may have heard something about it before then, but I don't remember that much before then.

Lightman:

But you're saying that it didn't strike you as serious a problem as the horizon problem?

Page:

Right.

Lightman:

Because you thought that there was just one number that had to be fixed at the Planck time.

Page:

Yes.

Lightman:

And how did you imagine that number would have been fixed?

Page:

I can't remember what I thought back then when I first heard of the problem, but I might have thought there's a quantum ensemble of universes. There are all these different wave components and omega might have a whole lot of different values, and maybe life can only exist in the ones in which omega is fairly close to one.

Lightman:

So you were really thinking about the anthropic principle at that point.

Page:

Well, I'm not sure that I thought about it that early. At least by the time that I could have been comparing the flatness problem to the horizon problem. I think by then I would have been more likely to think that maybe there's an anthropic explanation [for the flatness problem]. Not that I was sure, but "I thought the problem was less important than the others anyway, and so you'd have to do something very special to solve the other problems. So if you do that, the flatness problem falls out of the whole thing.

Lightman:

Let me move on to another issue. One of the things that I'm interested in is how physicists use metaphors and visualization in their work, if at all. You, of course, do a lot of work in the very early universe. Do you ever try to form a visual picture of the universe at a very early stage?

Page:

Well, when we're doing these path-integral calculations, you try to have various four-geometries that go into certain three-geometries. We [try] to draw diagrams, and we tend to throw [out] two dimensions. I'll visualize, say, the surface of a three- sphere. I'll just visualize that as a little line and then maybe the four-sphere or part of a four-sphere, whose boundaries is three-sphere, I can maybe think of as a little part of a bowl or cup or just a little sheet or something. So a lot of times we'll reduce the dimensions by two to draw these pictures. Then you have pictures of various universes connecting up. So I suppose there's a certain amount of visualization.

Lightman:

Do you ever try to picture the big bang?

Page:

I don't know, other than when I give relativity lectures on the big bang, or if I'm explaining the horizon problem. I'll draw a space-time diagram with time upward and space outward. I usually do this funny conformal business to get the light cones to be along 45-degree lines and the conforming lines vertical and then just draw some line across the bottom for the big bang.

Lightman:

Is that what you think up in your head as the big bang?

Page:

That's when I'm doing a classical picture. In the quantum picture, the concept of time is fuzzy back there, and the meaning of time is going to break down. Recently, I've perhaps had various visualizations in the sense that we've done a lot of trial calculations with a mini superspace model. One particular one is my favorite. It's greatly over-simplified, but it has enough to it that makes even it quite complex. We have a Friedmann- Robertson-Walker universe, which is governed by one scale parameter, say, for the size of the universe, and then one homogeneous scalar field. Then you could try to look for a wave function that obeys the Wheeler-DeWitt equation in this two-dimensional space. I could play around with diagrams with that, because it turns out there's a certain DeWitt metric on this space, which, in this case, actually is the same as one plus one dimensional flat. Lorentzian space in the right coordinates. And the allowed range for the coordinates means that you're in the interior of the light cone. Well, it really just means in the interior of two lines that open at 45 degrees... And then I can think about how classical solutions behave in this space and how they run around.

Lightman:

It sounds like you don't really visualize anything that corresponds to physical space.

Page:

Yes, not really. With quantum cosmology, you tend to think of how the wave functions behave, and then maybe wave packets. So I probably have more visualization of wave packets that might be describing these trajectories. But it's hard for me to visualize in more dimensions. I remember in one of my recent papers, I had something that described it in terms of three coupled first-order equations. Or you could describe [the trajectories of the wave packets] in terms of the geodesic equation with some funny metric — not the flat metric — but some conformally-related metric on this space. I said that another way of presenting this that is simpler for a relativist such as myself, who has a hard time visualizing in more dimensions than the surface of his retina, is to draw this as a geodesic equation on this two-dimensional space. I probably don't have much of a physical picture of that. Maybe if I think about stars forming and galaxies, explosions, [I can form pictures].

Lightman:

Well, that pretty much answers my question. Of course, we have photographs of some of those last things you mentioned.

Page:

Yes, of stars and galaxies, right.

Lightman:

At this stage in your career, do you have any preference for any particular kind of universe, an open versus a closed?

Page:

Open versus closed and all that sort of thing. Well, now this Hawking prescription so far has been given in the case of the three-dimensional space, which" is closed. In fact, the four-dimensional spaces that you put in the path integral are also compact, and it's only boundaries. So, I suppose just because we don't really know what to do if [the spaces are] non-compact maybe gives a certain amount of prejudice towards the ones that are compact. You get a finite action. In the back of my mind, I realize that is just a limitation of the current mathematics. But on the other hand, even with the compact ones, if it were a Friedmann-Robertson-Walker [space], it could be a three-torus, for example, and be spatially flat, or it could be k = -1, some hyperbolic space, with various identifications [making it compact].

Lightman:

Other than the Hawking-Hartle prescription, you don't have any other particular preference?

Page:

Probably not. I suppose I do believe in inflation at least enough to have some prejudice toward thinking that omega is likely to be very close to one, rather than, say, around a half or whatever the observational [result is]. So, if I had to bet on it, I would put more money on saying that more careful observations are going to find that [omega] is close to one, rather than it's going to end up being at a half. It seems very odd that [omega] would be so close to one and yet just now, in the present age, be drifting off. Unless the anthropic principle is the right argument for it. But somehow, if the anthropic thing were right, I'd expect [omega] to be more different from one than just a half. Maybe a tenth, or three. Steven Hawking and I wrote this paper,^[27] which is based on the crudity of some mini-superspace calculation, in which we predict that omega would be arbitrarily close to one, at least, if you ignored the fluctuations. That's going to differ maybe by one part in 10⁴ or something.

Lightman:

Let me ask you one last question, because I think we're running out of time. We've already been pretty speculative, but if you could design the universe any way that you wanted to, how would you do it?

Page:

I never particularly thought about that, because I've been thinking about how the [universe] could be. My knowledge of the mathematics that you need to get it in the state is sufficiently meager... It seems like we can have some guesses as to how this might work out, but how would I design it myself...

Lightman:

You can design it how you want to.

Page:

I can design it how I want to. I don't know. If I was going to do things any differently, the only things I would have any idea about would be more things on the human level. I mean, the Bible has some picture of heaven. One can imagine changing things like social injustices or eliminating diseases. But if I wanted to do this in some mathematical physics way, writing down a different Lagrangian, the trouble is [that] I have very little idea what the consequences of some of these equations are. Maybe can try to guess that the Lagrangian described by some superstring theory and maybe something like the Hartle-Hawking [boundary condition] is right, just because we have this universe to visualize. If I tried changing these, changing the state, changing the boundary conditions, it's very difficult for me to visualize what the outcome might be. To be honest, I guess I never really thought about trying to design the universe. [Laughs]

Lightman:

You've never thought about how you would design the universe? [laughs]

Page:

I suppose I was a bit daunted by the task. So it's a little hard for me to say. Of course, just on the human level, I can say there are other things, like the problem of evil. If I were [designing the universe], I might eliminate [evil], but on the other hand, maybe that wouldn't leave [living] beings. I don't know. Maybe [such beings] wouldn't have the capacity to respond as we do to God. I'm not quite sure what the consequences would be of changing things, and maybe it would turn out to be worse than what we have. I don't know. I'm slightly torn as to whether the universe God's created is the best possible one. But in a certain sense, though, I do know that this universe isn't perfect, that it's fallen. Part of it you can just say is an effect of man's sin on earth, and then greed and so on that people have. Now, to what extent this fallenness reflects itself in the whole physical universe, I'm not sure. [In the Bible], I think Paul writes that the whole universe is groaning since the creation, waiting for its redemption by Christ. The whole universe will be brought into the right relationship, which was lost as well. It won't just be humans that are pulled out of this situation, but in some sense the whole universe as well. I think that is a picture of heaven. So there's an image there that things could be better, or that things will be better in life with God, but exactly the characteristics of [that better universe are unclear]. I suppose in terms of physics, and so on, it's very nearly like ours. You just eliminate the evil. But, it's conceivable that it's altogether different.